Combined Spectral-Perturbation Approach for Systematic Mode Selection in Thermal Convection

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Zahir U. Ahmed ◽  
Bashar Albaalbaki ◽  
Roger E. Khayat
Keyword(s):  
Fluid Layer ◽  
Mode Selection ◽  
Galerkin Projection ◽  
Temperature Fields ◽  
Perturbation Approach ◽  
Critical Range ◽  
Expansion Coefficients ◽  
Convective State ◽  
Similarity And Difference ◽  
Spectral Perturbation

A nonlinear spectral approach is proposed to simulate the post critical convective state for thermogravitational instability in a Newtonian fluid layer heated from below. The spectral methodology consists of expanding the flow and temperature fields periodically along the layer, and using orthonormal shape functions in the transverse direction. The Galerkin projection is then implemented to generate the equations for the expansion coefficients. Since most of the interesting bifurcation picture is close to criticality, a perturbation approach is developed to solve the nonlinear spectral system in the weakly post critical range. To leading order, the Lorenz model is recovered. The problem is also solved using amplitude equations for comparison. The similarity and difference among the three models are emphasized.

A combined spectral-amplitude-perturbation approach for systematic mode selection in thermal convection

2015 ◽  
Vol 25 (4) ◽  
pp. 782-802 ◽  
Author(s):  
Mohammad Niknami ◽  
Zahir Ahmed ◽  
Bashar Albaalbaki ◽  
Roger E Khayat
Keyword(s):  
Nusselt Number ◽  
Thermal Convection ◽  
Fluid Layer ◽  
Mode Selection ◽  
Critical Rayleigh Number ◽  
Temperature Fields ◽  
Spectral Amplitude ◽  
Perturbation Approach ◽  
Content Type ◽  
Critical Range

Purpose – The post-critical convective state for Rayleigh-Benard (RB) convection is studied using a nonlinear spectral-amplitude-perturbation approach in a fluid layer heated from below. The paper aims to discuss these issues. Design/methodology/approach – In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A combined amplitude-perturbation approach is developed to solve the nonlinear spectral system in the post-critical range, even far from the linear stability threshold. Also, to leading order, the Lorenz model is recovered. Findings – It is found that very small Prandtl numbers (Pr < 0.1) can change the Nusselt number, when terms to O(ε5/2) and higher are considered. However, to lower orders the Prandtl number does not affect the results. Variation of the Nusselt number to different orders is found to be highly consistent. Comparison with experimental results is made and a very good qualitative agreement is observed, even far from the linear threshold. Originality/value – Unlike existing nonlinear formulations for RB thermal convection, the present combined spectral-perturbation approach provides a systematic method for mode selection. The number and type of modes to be included are directly related to the post-critical Rayleigh number. The method is not limited to the weakly nonlinear range.

Nonlinear thermal convection of a non-Fourier fluid

2016 ◽  
Vol 26 (3/4) ◽  
pp. 639-670 ◽  
Author(s):  
Rahim M Khorasany ◽  
Roger E Khayat ◽  
Mohammad Niknami
Keyword(s):  
Thermal Convection ◽  
Fluid Layer ◽  
Mode Selection ◽  
Critical Rayleigh Number ◽  
Perturbation Parameter ◽  
Temperature Fields ◽  
Process Time ◽  
Perturbation Approach ◽  
Content Type ◽  
Critical Range

Purpose – The purpose of this paper is to determine the thermo-gravitational convective state of a non-Fourier fluid layer of the single-phase-lagging type, heated from below. Unlike existing methodologies, the spectral modes are not imposed arbitrarily. They are systematically identified by expanding the spectral coefficients in terms of the relative departure in the post-critical Rayleigh number (perturbation parameter). The number and type of modes is determined to each order in the expansion. Non-Fourier effects become important whenever the relaxation time (delay in the response of the heat flux with respect to the temperature gradient) is of the same order of magnitude as process time. Design/methodology/approach – In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A perturbation approach is developed to solve the nonlinear spectral system in the post-critical range. Findings – The Nusselt number increases with non-Fourier effect as suggested in experiments in microscale and nanofluid convection. Originality/value – Unlike existing nonlinear formulations for RB thermal convection, the present combined spectral-perturbation approach provides a systematic method for mode selection.

Development of Convective Heat Transfer Near Suddenly Heated, Vertically Aligned Horizontal Wires

1987 ◽  
Vol 109 (4) ◽  
pp. 912-918 ◽  
Author(s):  
J. R. Parsons ◽  
M. L. Arey
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Fluid Layer ◽  
Convective Motion ◽  
Transient Behavior ◽  
Temperature Fields ◽  
Heat Sources ◽  
Transfer Coefficients ◽  
Vertically Aligned ◽  
The Wire

Experiments have been performed which describe the transient development of natural convective flow from both a single and two vertically aligned horizontal cylindrical heat sources. The temperature of the wire heat sources was monitored with a resistance bridge arrangement while the development of the flow field was observed optically with a Mach–Zehnder interferometer. Results for the single wire show that after an initial regime where the wire temperature follows pure conductive response to a motionless fluid, two types of fluid motion will begin. The first is characterized as a local buoyancy, wherein the heated fluid adjacent to the wire begins to rise. The second is the onset of global convective motion, this being governed by the thermal stability of the fluid layer immediately above the cylinder. The interaction of these two motions is dependent on the heating rate and relative heat capacities of the cylinder and fluid, and governs whether the temperature response will exceed the steady value during the transient (overshoot). The two heat source experiments show that the merging of the two developing temperature fields is hydrodynamically stabilizing and thermally insulating. For small spacing-to-diameter ratios, the development of convective motion is delayed and the heat transfer coefficients degraded by the proximity of another heat source. For larger spacings, the transient behavior approaches that of a single isolated cylinder.

On Low-Dimensional Galerkin Modeling of Confined Twin-Jet Flow and Heat Transfer

2001 ◽  
Author(s):  
H. Gunes ◽  
K. Gocmen ◽  
L. Kavurmacioglu
Keyword(s):  
Heat Transfer ◽  
Jet Flow ◽  
Basis Functions ◽  
Galerkin Projection ◽  
Temperature Fields ◽  
Transitional Flow ◽  
Flow And Heat Transfer ◽  
Galerkin Models ◽  
Velocity And Temperature Fields ◽  
Low Dimensional

Abstract The two-dimensional incompressible non-isothermal confined twin-jet flow has been numerically studied in the transitional flow regime by a finite volume technique. Results have been obtained for the velocity and temperature distributions close to the onset of temporal oscillations. Next, the proper orthogonal decomposition (POD) is applied to the instantaneous flow and temperature data to obtain POD-based basis functions for both velocity and temperature fields. These basis functions are capable to identify the coherent structures in the velocity and temperature fields. The low-dimensional Galerkin models of the full Navier-Stokes and energy equations are constructed by the Galerkin projection onto basis functions. Since the low-dimensional Galerkin models are much easier to analyze than the full governing equations, basic insights into important mechanisms of dynamically complex flow and heat transfer (e.g. flow instabilities) can be easily studied by these models. The numerical implications, the validity of the models and their performance characteristics are discussed.

Flows in Rotating Cylinders With a Porous Lining

2007 ◽  
Author(s):  
M. Subotic ◽  
F. C. Lai
Keyword(s):  
Porous Layer ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Outer Cylinder ◽  
Tangential Velocity ◽  
Darcy Number ◽  
Temperature Fields ◽  
Rotating Cylinders ◽  
Press Fit ◽  
Porous Sleeve

Flow and temperature fields in an annulus between two rotating cylinders have been examined in this study. While the outer cylinder is stationary, the inner cylinder is rotating with a constant angular speed. A homogeneous and isotropic porous layer is press-fit to the inner surface of the outer cylinder. The porous sleeve is saturated with the fluid that fills the annulus. The Brinkman-extended Darcy equations are used to model the flow in the porous layer while Navier-Stokes equations are used for the fluid layer. The conditions applied at the interface between the porous and fluid layers are the continuity of temperature, heat flux, tangential velocity and shear stress. Analytical solutions have been attempted. Through these solutions, the effects of Darcy number, Brinkman number, and porous sleeve thickness on the velocity profile and temperature distribution are studied.

scholarly journals Convective fluid flow and heat transfer in a vertical rectangular duct containing a horizontal porous medium and fluid layer

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
J.C. Umavathi ◽  
O. Anwar Beg
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Numerical Solutions ◽  
Fluid Layer ◽  
Rectangular Cross Section ◽  
Volumetric Flow Rate ◽  
Immiscible Fluids ◽  
Temperature Fields ◽  
Numerical Code ◽  
Content Type

Purpose The purpose of this paper is to investigate thermally and hydrodynamically fully developed convection in a duct of rectangular cross-section containing a porous medium and fluid layer. Design/methodology/approach The Darcy–Brinkman–Forchheimer flow model is adopted. A finite difference method of second-order accuracy with the Southwell-over-relaxation method is deployed to solve the non-dimensional momentum and energy conservation equations under physically robust boundary conditions. Findings It is found that the presence of porous structure and different immiscible fluids exert a significant impact on controlling the flow. Graphical results for the influence of the governing parameters i.e. Grashof number, Darcy number, porous media inertia parameter, Brinkman number and ratios of viscosities, thermal expansion and thermal conductivity parameters on the velocity and temperature fields are presented. The volumetric flow rate, skin friction and rate of heat transfer at the left and right walls of the duct are also provided in tabular form. The numerical solutions obtained are validated with the published study and excellent agreement is attained. Originality/value To the author’s best knowledge this study original in developing the numerical code using FORTRAN to assess the fluid properties for immiscible fluids. The study is relevant to geothermal energy systems, thermal insulation systems, resin flow modeling for liquid composite molding processes and hybrid solar collectors.

The Influence of the Magnetic Boundary Conditions on the Nature of Astrophysical Convection

1983 ◽  
Vol 5 (2) ◽  
pp. 172-173
Author(s):  
J. M. Lopez ◽  
J. O. Murphy
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Fluid Layer ◽  
Heat Energy ◽  
Time Dependent ◽  
Linear Partial Differential Equations ◽  
Convective Motions ◽  
Convective State ◽  
Field Disturbance ◽  
The Magnetic Field

The relevance of the results for the total heat energy transported across a fluid layer by convective motions, obtained from the time integrations of the set of non-linear partial differential equations for hydromagnetic convection, has already been designated in a previous contribution (Lopez and Murphy 1982). Some differences in the form of the boundary conditions adopted for the magnetic field disturbance, H, have been noted in other publications where the interaction of convection and a magnetic field has also been considered. The solutions of the time-dependent equations, referenced above, illustrate that the magnetic boundary conditions have a determining role in the resultant convective state for some ranges of values in parameter space.

Stochastic analysis of two-phase flow in porous media: I. Spectral/perturbation approach

1995 ◽  
Vol 19 (3) ◽  
pp. 233-259 ◽  
Author(s):  
Ching-Min Chang ◽  
Marian W. Kemblowski ◽  
Jagath J. Kaluarachchi ◽  
Alaa Abdin
Keyword(s):  
Porous Media ◽  
Stochastic Analysis ◽  
Two Phase Flow ◽  
Flow In Porous Media ◽  
Perturbation Approach ◽  
Phase Flow ◽  
Two Phase ◽  
Spectral Perturbation
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